11 limit blackjack lattice

Since my piece for trombone and electronics in the blackjack scale is
just about finished, (I will post it someplace on the Web when done
in just a MIDI version until it's performed) I am thinking ahead to
some other work in the blackjack scale....

I would like to focus on a purely electronic work emphasizing
harmony...

I've been working with Paul Erlich's great color 7-limit blackjack
lattice, but Paul has been suggesting that I explore 11-limit as
well... for common-tone harmonies and such like.

It looks like I could devote about 8 MIDI voices to harmony, so I can
surely do more than tetrads this time.

Paul suggested that perhaps Graham Breed had some ideas regarding
practical visualizations of an 11 limit blackjack lattice.

Is that true, Graham?? Paul says you have done this before.

Of course, it would be important that one could clearly see where the
consonant connections are...

Is this possible???

Thanks!

_________ ________ ______
Joseph Pehrson

In-Reply-To: <9jqaor+kpjr@eGroups.com>
Joseph Pehrson wrote:

> Paul suggested that perhaps Graham Breed had some ideas regarding
> practical visualizations of an 11 limit blackjack lattice.
>
> Is that true, Graham?? Paul says you have done this before.

See <http://x31eq.com/decimal_lattice.htm>. That uses decimal
notation, you can see the conversion charts at
<http://x31eq.com/miracle/conversion.html>.

It makes sense with the 24 note keyboard mapping I gave in
</tuning/topicId_22183.html#22183>. There, the numerals
refer to the black notes starting on C#, a ^ means "move up the keyboard a
step" and a v means "move down the step" where that doesn't contradict
with the previous rule. You get a whole Blackjack with some bonuses.

I found a strip of masking tape with the numbers on it very useful in
getting the hang of this. You should be able to find the pump-progression
in decimal notation so you can find it on the keyboard and lattice. See
also the lattice here </tuning/topicId_21957.html#21970>
which uses meantone-enharmonic notation, if that makes it easier for you.

Graham

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_26488.html#26493

> In-Reply-To: <9jqaor+kpjr@e...>
> Joseph Pehrson wrote:
>
> > Paul suggested that perhaps Graham Breed had some ideas regarding
> > practical visualizations of an 11 limit blackjack lattice.
> >
> > Is that true, Graham?? Paul says you have done this before.
>
> See <http://x31eq.com/decimal_lattice.htm>. That uses
decimal
> notation, you can see the conversion charts at
> <http://x31eq.com/miracle/conversion.html>.
>
> It makes sense with the 24 note keyboard mapping I gave in
> </tuning/topicId_22183.html#22183>. There, the
numerals
> refer to the black notes starting on C#, a ^ means "move up the
keyboard a
> step" and a v means "move down the step" where that doesn't
contradict
> with the previous rule. You get a whole Blackjack with some
bonuses.
>
> I found a strip of masking tape with the numbers on it very useful
in
> getting the hang of this. You should be able to find the pump-
progression
> in decimal notation so you can find it on the keyboard and
lattice. See
> also the lattice here
</tuning/topicId_21957.html#21970>
> which uses meantone-enharmonic notation, if that makes it easier
for you.
>
>
> Graham

Hi Graham!

Thanks for the help... I'm going to try to make some sense of this...

______ _______ ______
Joseph Pehrson

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <9jqaor+kpjr@e...>
> Joseph Pehrson wrote:
>
> > Paul suggested that perhaps Graham Breed had some ideas regarding
> > practical visualizations of an 11 limit blackjack lattice.
> >
> > Is that true, Graham?? Paul says you have done this before.
>
> See <http://x31eq.com/decimal_lattice.htm>.

The problem with that is, it's very difficult to see where the 11-
limit connections are, and (if I'm not mistaken), where the 11-limit
connections _aren't_.

I think what Joseph wants is something similar to the color 3D 7-
limit lattice I created for blackjack. If you haven't seen that, go to

/tuning/files/perlich/scales/

download

bjlatt.ZIP

and look at

blackjack0.bmp

(I can provide a .jpg or .gif of this if anyone wishes).

We'd want to do something similar for 11-limit. Maybe we can make use
of "impossible" 3D shapes to make a movement of 2401:2400 come back
to the same point, as it does in Graham's lattice. We'd need curved
connectors for 9:8s, since they span over two 3:2s -- see Dave
Keenan's lattices. Dave, any ideas?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> We'd want to do something similar for 11-limit. Maybe we can make
use
> of "impossible" 3D shapes to make a movement of 2401:2400 come back
> to the same point, as it does in Graham's lattice. We'd need curved
> connectors for 9:8s, since they span over two 3:2s -- see Dave
> Keenan's lattices.

Not only that. You'd need curved connectors for 2:3s since they span
two 9:11s. That would be way too cluttered. Best just show those once
(in the legend) and let the reader imagine them on the actual lattice.

> Dave, any ideas?

I worked on it a bit a while ago (showing all 11-limit "consonances"
except the curved ones). I came up with this 2D lattice.

7
|
5 .
| |
1--.--3--.--9-11

where 1:7, 3:5, 3:7, 5:7, 7:11 are also connected by straight lines. 7
colours required. The notes are on a golden-rectangular grid. The
golden rectangles are higher than they are wide.

224:225 and 243:245 both vanish in this lattice (as they do in
Miracle).

Blackjack then looks like this (two periods shown):

5> 8> 1 4 7 0< 3<

6> 9> 2 5 8 1< 4<

4> 7> 0 3 6 9 2<

5> 8> 1 4 7 0< 3<

6> 9> 2 5 8 1< 4<

4> 7> 0 3 6 9 2<

I'll have to leave it for someone else to translate the note-names
into Josephs favourite 72-EDO subset and add the coloured lines.

-- Dave Keenan

Sorry. I meant 242:243, not 243:245.

And yes, I really did intend to leave out the 5:9 and 5:11 lines. In
blackjack there are only two of the former and none of the latter. I
suppose you can put the 5:9's in using an eighth colour if you want,
but I think it will be cluttered enough (maybe just show it on the
legend along with the curved 1:3s, 1:9s, 3:11s and 1:11s.).

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_26488.html#26510

>
> I worked on it a bit a while ago (showing all 11-
limit "consonances"
> except the curved ones). I came up with this 2D lattice.
>
> 7
> |
> 5 .
> | |
> 1--.--3--.--9-11
>
> where 1:7, 3:5, 3:7, 5:7, 7:11 are also connected by straight
lines. 7
> colours required. The notes are on a golden-rectangular grid. The
> golden rectangles are higher than they are wide.
>
> 224:225 and 243:245 both vanish in this lattice (as they do in
> Miracle).
>
> Blackjack then looks like this (two periods shown):
>
> 5> 8> 1 4 7 0< 3<
>
> 6> 9> 2 5 8 1< 4<
>
> 4> 7> 0 3 6 9 2<
>
> 5> 8> 1 4 7 0< 3<
>
> 6> 9> 2 5 8 1< 4<
>
> 4> 7> 0 3 6 9 2<
>
> I'll have to leave it for someone else to translate the note-names
> into Josephs favourite 72-EDO subset and add the coloured lines.
>
> -- Dave Keenan

Thanks, Dave, for your help with this. Yes, that would be helpful...

Of course, frankly, I haven't even fully explored harmony with the 7-
limit lattice, but 11-limit is certainly an area to explore at some
point....

________ ________ _____
Joseph Pehrson

Here it is with colour and 6*12-tET note names. I don't think it
really works, but you be the judge.

http://dkeenan.com/Music/Miracle/Blackjack11Lattice.gif

I think we're up against Wilson's "lattice barrier" and might do well
to study his solutions.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_26488.html#26530

> Here it is with colour and 6*12-tET note names. I don't think it
> really works, but you be the judge.
>
> http://dkeenan.com/Music/Miracle/Blackjack11Lattice.gif
>
> I think we're up against Wilson's "lattice barrier" and might do
well
> to study his solutions.
>
> -- Dave Keenan

Hi Dave...

Thanks for this!

It's a little *intense*.... I'll see what I can do with it...

_______ _______ ___________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Hi Dave...
>
> Thanks for this!
>
> It's a little *intense*.... I'll see what I can do with it...
>
It's pretty cluttered, and it doesn't seem that the curved lines are
in there yet . . . a 3-D representation like what I did in the 7-
limit case would seem to be essential for seeing chords within the
tangled mess . . . thanks for taking this first step, though, Dave!